Divisors of 1824: All 24 Factors

Divisors (Factors) Calculator

Use the calculator above to find all divisors (also called factors) of any positive integer up to 4,782,969. Beyond the divisor list, this tool also shows divisor pairs, the sum and count of divisors, prime factorization, and number properties (prime, perfect square, perfect number).

All Divisors of 1824

The number 1824 has 24 divisors:

1,  2,  3,  4,  6,  8,  12,  16,  19,  24,  32,  38,  48,  57,  76,  96,  114,  152,  228,  304,  456,  608,  912,  1824

Divisor Pairs of 1824

Each pair multiplies to 1824:

Number of Divisors

The number 1824 has 24 divisors, written as τ(1824) = 24 in number theory.

Sum of Divisors

σ(1824) = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 19 + 24 + 32 + 38 + 48 + 57 + 76 + 96 + 114 + 152 + 228 + 304 + 456 + 608 + 912 + 1824 = 5040

Prime Factorization of 1824

See the full prime factorization calculator →

Properties of 1824

• 1824 is composite.
• 1824 is not a perfect square.
• Number of divisors: 24.
• Sum of divisors: 5040.

Common Divisors with Another Number?

Looking for the divisors that 1824 shares with another number? Use our Greatest Common Factor (GCF) calculator — it finds all common divisors and the largest one.

Step-by-Step: How to Find the Divisors of 1824

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √1824 ≈ 42.71. If i divides 1824, then both i and 1824/i are divisors.

1. 1 divides 1824 (1824 ÷ 1 = 1824) → pair (1, 1824)
2. 2 divides 1824 (1824 ÷ 2 = 912) → pair (2, 912)
3. 3 divides 1824 (1824 ÷ 3 = 608) → pair (3, 608)
4. 4 divides 1824 (1824 ÷ 4 = 456) → pair (4, 456)
5. 6 divides 1824 (1824 ÷ 6 = 304) → pair (6, 304)
6. 8 divides 1824 (1824 ÷ 8 = 228) → pair (8, 228)
7. 12 divides 1824 (1824 ÷ 12 = 152) → pair (12, 152)
8. 16 divides 1824 (1824 ÷ 16 = 114) → pair (16, 114)
9. 19 divides 1824 (1824 ÷ 19 = 96) → pair (19, 96)
10. 24 divides 1824 (1824 ÷ 24 = 76) → pair (24, 76)
11. 32 divides 1824 (1824 ÷ 32 = 57) → pair (32, 57)
12. 38 divides 1824 (1824 ÷ 38 = 48) → pair (38, 48)
13. Collect all unique values: {1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912, 1824} — total 24 divisors.
14. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 19 + 24 + 32 + 38 + 48 + 57 + 76 + 96 + 114 + 152 + 228 + 304 + 456 + 608 + 912 + 1824 = 5040.

Nearby Examples

Related Operations for 1824

• Multiples of 1824 — "outward" complement; M is a multiple of 1824 ⇔ 1824 is a divisor of M
• 1824 Prime Factorization — decompose into prime building blocks
• Find GCF of 1824 and another number
• Find LCM of 1824 and another number
• Is 1824 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

What Is a Divisor?

A divisor (also called a factor) of a positive integer n is any positive integer d such that n ÷ d has no remainder. In other words, d divides n evenly.

Every positive integer n has at least two divisors: 1 and n itself (with 1 being the trivial case of having only itself). Numbers with exactly 2 divisors are prime; numbers with 3 or more divisors are composite.

Why use this calculator? Beyond just listing divisors, this tool computes the sum σ(n), the count τ(n), prime factorization, divisor pairs (useful for visual learners and factoring problems), and detects whether n is a prime, a perfect square, or a perfect number.

References

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

Divisors Calculation Examples

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